{
  "id": "1208.2905",
  "version": "v2",
  "published": "2012-08-14T15:46:12.000Z",
  "updated": "2019-12-13T14:19:21.000Z",
  "title": "On some exact solutions of heavenly equations in four dimensions",
  "authors": [
    "Ł. T. Stȩpień"
  ],
  "categories": [
    "math-ph",
    "gr-qc",
    "math.MP"
  ],
  "abstract": "Some new classes of exact solutions (so-called functionally-invariant solutions) of the elliptic and hyperbolic complex Monge-Amp$\\grave{e}$re equations and of the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation, evolution form of second heavenly equation, general heavenly equation, real general heavenly equation and one of the real sections of general heavenly equation, are found. Besides non-invariance of these found classes of solutions has been investigated. These classes of solutions determine the new classes of metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to found classes, has been also formulated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-14T15:46:12.000Z",
      "title": "Some new classes of exact solutions of the heavenly equations in four dimensions",
      "abstract": "Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge-Amp$\\`{e}$re equations, the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation and evolution form of second heavenly equation are found. Besides non-invariance of these found classes of solutions has been investigated. These classes of solutions determine the new classes of heavenly metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to found classes, has been also formulated.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2019-12-13T14:19:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact solutions",
      "second heavenly equation",
      "dimensions",
      "hyperbolic complex monge-amp",
      "evolution form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1127494,
      "adsabs": "2012arXiv1208.2905S"
    }
  }
}